Biol 7932, 22 October 2024
2024-10-22
Example: Common Terns (Sterna hirundo) move between colonies (Dittman et. al. 2005, 2007)
Do sub-adult Leach’s storm-petrels attend multiple breeding colonies?
Do they visit the same colony multiple times?
Can we identify characteristics of individuals that predict colony attendance behaviour?
Pros:
Limitations
All captured birds (n = 245):
All tagged birds (n = 28):
VHF data:
| Variable | Symbol | Type | Role | Factor Type |
|---|---|---|---|---|
| Returned | R | Binomial | Response | NA |
| Wing chord | WC | Ratio | Explanatory | Fixed |
| Weight | WT | Ratio | Explanatory | Fixed |
\[ R = \beta_0 + \beta_{WC}WC + \beta_{WT}WT + \beta_{WC * WT}WC*WT + \epsilon \] Degrees of Freedom:
\[ 28 = 1 + 1 + 1 + (1)(1) + 24 \]
morphology_model <- glm(data = banding_data, R ~ weight+wing_chord+weight*wing_chord, family = binomial(link="logit"))
anova(morphology_model)Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
weight 1 0.06554 26 35.099 0.7979
wing_chord 1 0.34723 25 34.752 0.5557
weight:wing_chord 1 0.60330 24 34.149 0.4373
The interaction term appears trivial, so we can drop it and re-write the model:
\[ R = \beta_0 + \beta_{WC}WC + \beta_{WT}WT + \epsilon \]
Not really.
Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
weight 1 0.06554 26 35.099 0.7979
wing_chord 1 0.34723 25 34.752 0.5557
weight:wing_chord 1 0.60330 24 34.149 0.4373
\[ G = \Delta Deviance \]
\[ LR = e^{G/2} \]
\[ LR = e^{1.016/2} \] \[ LR = 1.662 \]
Not convincing! There isn’t compelling evidence that morphology had an effect on whether or not tagged birds returned.
| Variable | Symbol | Type | Role | Factor Type |
|---|---|---|---|---|
| Returned | R | Binomial | Response | NA |
| Handling Time | HT | Ratio | Explanatory | Fixed |
| Second Handler (HA, DW, or SW) | HA | Nominal | Explanatory | Random |
\[ R = \beta_0 + \beta_{HT}HT + \beta_{HA}HA + \beta_{HT * HA}HT * HA + \epsilon \]
Degrees of Freedom
\[ 28 = 1 + (3-1) + (1)(3-1) + 23 \]
Again, not really.
Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
handling_time 1 0.5688 26 34.596 0.450745
second_handler 2 3.0734 24 31.523 0.215089
handling_time:second_handler 2 12.8555 22 18.667 0.001616 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
A significant interaction effect!
Handler likely has an effect on handling time; not a surprise.
I am mainly interested in handling time, so I’ll assess that on its own.
Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
handling_time 1 0.56878 26 34.596 0.4507
\[ LR = 1.329 \]
There is not compelling evidence that handling time affected whether or not a tagged bird returned.
| Variable | Symbol | Type | Role | Factor Type |
|---|---|---|---|---|
| Returned | R | Binomial | Response | NA |
| Island of Capture (Great or Gull) | Is | Nominal | Explanatory | Fixed |
\[ R = \beta_0 + \beta_{Is}Is + \epsilon \]
Degrees of Freedom:
\[ 28 = 1 + (2-1) + 26 \]
Weird!
Again, not much better.
Analysis of Deviance Table
Model: binomial, link: logit
Response: R
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL 27 35.165
location 1 2.2078 26 32.957 0.1373
\[ LR = 3.0162 \]
There is not convincing evidence that island of capture affected whether tagged birds returned.
(if anyone is interested, if you set this up as a classic Chi-squared test, the p-value is 0.09.)
Project supervised by David Wilson
Environment & Climate Change Canada (especially Dave Fifield and Sabina Wilhelm) graciously allowed us to use their VHF receivers
Fieldwork help & Photography: Kobe Loveless, Hallie Arno, Sabina Wilhelm, Chris Ward, Gill Holmes
Project funding from NSERC Discovery Grant to Dr. Wilson